Tw. Castigliano: $\varphi_{A} = \frac{\partial v}{\partial M^{*}}|M^{*} = 0 = \int_{0}^{L}\frac{M\left( x \right)*\frac{\partial M}{\partial M^{*}}\text{dx}}{\text{EI}}$ Warunki brzegowe dla ugięcia: 1. U1(o)=0; 2.u2(2L)=up(l), 3. $EA = \frac{\text{du}}{\text{dx}}\left| x = 2L = 2EA\frac{\text{du}}{\text{dx}} \right|x = L$ 4.$\ \left| 2EA\frac{\text{du}}{\text{dx}} \right|x = 3L = 2P$. Przekrój kołowy: $\tau_{\text{xz}} = \frac{4}{3}\frac{\text{Tz}}{\pi r^{2}}$